Transient analysis of Bang-Bang phase locked loops without cycle slipping for frequency step inputs

In this paper an exact transient analysis of Bang-Bang PLLs (BBPLLs), as a nonlinear system, is presented. The proposed analysis considers the input step in frequency. The results contain all important times, the related VCO control voltage and output excess phase. We considered frequency steps in which BBPLL does not experience cycle slipping. We could obtain an expression for maximum frequency step size in which cycle slipping does not occur. To evaluate the proposed analysis, many simulations are performed using MATLAB SIMULINK where all show very high accuracy of the proposed equations.